Experimental and Theoretical Analysis of Nanotransport in

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Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function Zuoti Xie,‡,† Ioan Bâldea,*,§,† Christopher Smith,‡ Yanfei Wu,‡ and C. Daniel Frisbie*,‡ ‡

Department of Chemical Engineering and Materials Science and Department of

Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States ¶§

Theoretische Chemie, Universität Heidelberg, INF 229, D-69120 Heidelberg, Germany

and National Institute of Lasers, Plasma and Radiation Physics, Institute of Space Science, POB MG-23 RO 077125, Bucharest, Romania. † Equal contribution *To whom correspondence should be addressed E-mail: [email protected]; [email protected]

ABSTRACT: We report the results of an extensive investigation of metal-moleculemetal tunnel junctions based on oligophenylene dithiols (OPDs) bound to several types of electrodes (M1−S−(C6H4)n−S−M2, with 1 ≤ 𝑛 ≤ 4 and M1,2 =Ag, Au, Pt) to examine the impact of molecular length (n) and metal work function (Φ) on junction properties. Our investigation includes (1) measurements by scanning Kelvin probe microscopy (SKPM) of electrode work function changes (∆Φ = Φ𝑆𝐴𝑀 − Φ) caused by chemisorption of OPD self-assembled monolayers (SAMs), (2) measurements of junction current-voltage (𝐼 − 𝑉) characteristics by conducting probe atomic force microscopy (CP-AFM) in the linear and nonlinear bias ranges, and (3) direct quantitative analysis of the full 𝐼 − 𝑉 curves. Further, we employ transition voltage spectroscopy (TVS) to estimate the energetic

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alignment 𝜀ℎ = 𝐸𝐹 − 𝐸𝐻𝑂𝑀𝑂 of the dominant molecular orbital (HOMO) relative to the Fermi energy 𝐸𝐹 of the junction. Where photoelectron spectroscopy data are available, the 𝜀ℎ values agree very well with those determined by TVS. Using a single-level model, which we justify via ab initio quantum chemical calculations at post-DFT level and additional UV-visible absorption measurements, we are able to quantitatively reproduce the 𝐼 − 𝑉 measurements in the whole bias range investigated (~1.0 − 1.5 V) and to understand the behavior of 𝜀ℎ and (contact coupling strength) extracted from experiment. We find that Fermi level pinning induced by the strong dipole of the metal-S bond causes a significant shift of the HOMO energy of an adsorbed molecule, resulting in 𝜀ℎ exhibiting a weak dependence with the work function Φ. Both of these parameters play a key role in determining the tunneling attenuation factor (𝛽) and junction resistance (R). Correlation among , 𝑅 , transition voltage ( 𝑉𝑡 ) and 𝜀ℎ and accurate simulation provide a remarkably complete picture of tunneling transport in these prototypical molecular junctions.

KEYWORDS: molecular electronics, molecular junctions, tunneling, charge transport, oligophenylene dithiol, work function, transport model.

Molecular electronics research is driven by the potential for molecular level engineering of electronic function in new nano-devices and by a desire for better understanding of charge transport mechanisms in molecular systems.1–21 Over the past 15 years, one of the main challenges in molecular electronics, at least from the experimentalist’s viewpoint, has been the lack of easily accessible quantitative models for the current-voltage (I-V)

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characteristics of molecular tunnel junctions. Conventional density functional theory (DFT) calculations, which represent the vast majority of the theoretical studies on molecular transport,19,22–33 are able to provide important information, e.g. on molecular conformation and contact topology. However, these calculations cannot be implemented by the non-expert. On the other hand, simple analytical theories such as the Simmons model for “square barrier” tunneling,34 while relatively simple to understand, have been shown repeatedly to be a poor description for molecular junctions, largely because the chemical nature of the constituent molecules is not accounted for.34–39 Indeed, the Simmons picture, if it applied, would be a rather uninteresting model for molecular electronics because the details of molecular structure are lumped into an aggregate barrier, providing no real insight into how tunnel currents can be manipulated precisely by chemistry.35,37,39 (In addition, the Simmons model as applied to charge transport is based on a defective mathematical approximation, as shown recently.40) The field has needed a more accurate analytical model, accessible to experimentalists and justifiable microscopically, in which quantitative fits to the transport data allow convenient extraction of parameters such as the HOMO (or LUMO) position, the transmission efficiency, and the strength of electronic coupling to the contacts. This information can then be employed in the design of new systems with rationally tuned transport characteristics. The model we employ here to analyze our transport data is based on a single level (Newns-Anderson41) description. As discussed in detail below (see Figure 2 and Remarks on the Theoretical Modeling in the Supporting Information (SI)), the fact that a single molecular orbital (namely, the HOMO) dominates the charge transport through the

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present junctions is justified microscopically (i) via equation-of-motion coupled-cluster singles and doubles calculations of the lowest ionization potentials (EOM-IP-CCSD) 42,43 at post DFT level, which represent the state-of-the-art of quantum chemistry for the molecular sizes considered, (ii) by additional UV-visible absorption experiments, and, last but not least, (iii) by direct comparison with UPS data,44 in cases where the latter are available (cf. Table 2). Thus, the simple one level model we employ here is not merely a convenient picture among many other off-resonant tunneling mechanisms,15 but it is a logical choice, and we demonstrate below that it provides an excellent overall quantitative description of a variety of experiments. Within this single-level model, a series of simple analytical formulas have been deduced recently,45–48 which are useful to describe the off-resonant, coherent tunneling typical of the vast majority of molecular junctions. Besides the zero-bias resistance R, 𝜀ℎ = 𝐸𝐹 − 𝐸𝐻𝑂𝑀𝑂 (the HOMO position with respect to the Fermi level EF) is a basic quantity of this approach.47 In a non-resonant situation (which turned out to be the case for all our junctions), 𝜀ℎ can be found straightforwardly from the minimum V=Vt in a Fowler-Nordheim (F-N) plot of the same I-V characteristic. The transition voltage Vt is a characteristic voltage evident by inspection of the F-N plot, that can be related analytically to 𝜀ℎ (see Eqs. (4) and (S2), and Transition Voltage Spectroscopy

5,44,49,50

).

This in turn means that, in cases (and all junctions investigated in this study belong to this category) where biases (at least slightly) above Vt can be accessed experimentally, 𝜀ℎ is not needed as an adjustable parameter in the fit of the full I-V characteristics. Rather, it is determined from the F-N plot and then  (width parameter related to molecule-electrode couplings, cf. Section Basic Working Equations) is adjusted to provide the complete fit.

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Agreement between theory and experiment is very good in the handful of cases addressed so far,45–48,51 and the overall approach is appealing because it is easy to implement and yields important molecule and contact-specific electronic structure information. In this paper, we describe an extensive experimental and theoretical investigation of a benchmark molecular electronics system, namely oligophenylene dithiols (OPDs) between metals, as a function of molecular length (up to four phenylene rings) and contact work function, Figure 1. This work builds on previous studies by our research group of oligoacene thiols and dithiols44,52 and alkane thiols and dithiols,35,53–55 as well as on work done by other groups on various molecules.1,7,30,56–66 To our knowledge, the effect of the contact work function and the related Fermi level pinning has not been addressed before for OPD junctions. Such studies, following earlier work on bondpolarization at metal surfaces,67,68 are important for OPD-based junctions; the OPDmolecules have a degree of aromaticity significantly different from the oligoacene molecules studied in our group,44 and the degree of pinning can vary from one moleculeelectrode pair to another. Another key difference here from our earlier work is that we are able to understand the full I-V behavior of the junctions quantitatively (up to ±1.5 V). Using the simple analytical model mentioned above and described in more detail below, we are able to extract 𝜀ℎ and  of molecular junctions based on four different OPDs and different combinations of Ag, Au, and Pt contacts, a total of 12 distinct metal-molecule-metal junctions. The theory agrees with experiment in all cases. Our investigation (1) adds to the growing body of evidence that molecular junction transport characteristics can be accurately modeled by an analytical theory; (2) it provides the most comprehensive

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analysis yet of the OPD system; (3) it confirms the important role of Fermi-level pinning on the transport and electronic characteristics of molecular junctions with metal-thiolate contacts; (4) it solidifies the utility of Transition Voltage Spectroscopy (TVS) for quantitative 𝐼 − 𝑉 analysis. In the most general sense, we believe that the present work is

A

B

I

CP-AFM tip S

S

n

S

n

n

S S S Metals: Ag, Au and Pt

n=1, 2, 3, 4

Figure 1: Schematic representation of the conducting probe atomic force microscopy (CP-AFM) setup. A metal-coated (Ag, Au, Pt) AFM tip is brought into contact with a SAM of oligophenylene dithiols (OPDs) of various lengths on a metal coated substrate. The tip-SAM contact area is ~40 nm2.

an example of both the high quality data that can be obtained for molecular tunnel junctions and the ability of theory to accurately model the results and return key transport parameters.

Results and Discussion As shown below, like in other cases,32,46–48,51,69 the single-level model with Lorentzian transmission (also known as the Newns-Anderson model41,70–72) provides an appropriate framework for analyzing all the experimental data on the transport through

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CP-AFM molecular junctions based on oligophenylene dithiols reported in this study. As already noted in the introduction, we adopt this model not because of its simplicity but rather because, for these junctions, it has a solid microscopic justification; the dominant role of the HOMO is visualized in Figure 2, which depicts the LUMOs much more distant from the Fermi energy and the (HOMO-1) orbitals are also sufficiently far away. Thus, the charge transport is described as a specific off-resonant coherent tunneling process (see also Section Remarks on the Theoretical Modeling in the SI for further details) mediated by the dominant molecular orbital, which is characterized by an energy offset 𝜀ℎ = 𝐸𝐹 − 𝐸𝐻𝑂𝑀𝑂 relative to the electrodes’ equilibrium (i.e. zero bias V=0) Fermi energy EF. Below we describe the key equations. Basic Working Equations. In cases (like the present and other cases32,45–48) where the energy offset 𝜀ℎ is sufficiently larger than the contact coupling strengths (also referred to as level width parameters) Γ𝑠,𝑡 determined by the molecular coupling to the substrate (s) and tip (t) [more precisely to order 𝑂(𝛤𝑠 𝛤𝑡 /𝜀ℎ2 )], and for biases V not too high (say 𝑒|𝑉| ≲ 1.5𝜀ℎ ), particularly simple analytical formulas have been deduced.47 The current I through a single molecule can be expressed 𝜀2

ℎ 𝐼1 = 𝐺1 𝑉 𝜀2 −(𝑒𝑉/2) 2

(1)

ℎ

where the zero-bias conductance of a single molecule is given by 𝐺1 = 𝐺0

Γ𝑠 Γ𝑡

(2)

2 𝜀ℎ

𝐺0 = 2𝑒 2 /ℎ = 77.48𝜇𝑆 being the conductance quantum. In general, an applied bias can shift the molecular orbital energy 𝜀ℎ → 𝜀ℎ (𝑉) = 𝜀ℎ − 𝛾𝑒𝑉

(3)

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A nonvanishing voltage division factor yields an asymmetric 𝐼 − 𝑉 curve [𝐼(𝑉) ≠

Figure 2: Microscopic justification of the single level ("only HOMO") model used to interpret the present transport data. The diagram presents the energies of relevant molecular orbitals for Pt/OPDn/Pt junctions. The alignment of the HOMOs with respect to the metallic Fermi level are given by the εh-values of Table 1, the energy differences between HOMO and HOMO-1 (equal to the differences between the green and red lines of Figure 8A) have been obtained via EOM-IP-CCSD quantum chemical calculations, and optical gaps extracted from UV/visible absorption data (Fig. S5) have been utilized as estimations for the LUMO positions.

−𝐼(−𝑉)] and transition voltages depending on polarity bias (𝑉𝑡+ ≠ −𝑉𝑡− ). Because this asymmetry is insignificant for the 𝐼 − 𝑉 curves measured by us (see Figure 5, Figure 9, and Figure S8, Figures S10-S12, and the 𝑉𝑡± values of Table 1), analytical formulas have been derived wherein 0 can be used safely, e.g., for the transition voltage Vt = 𝑉𝑡+ = −𝑉𝑡− 45,47 and 𝑒𝑉𝑡 = 2𝜀ℎ /√3.

(4)

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To obtain the 𝜀ℎ estimates (given in Table 1) more accurately, we employed in fact Eq. (S2), which generalizes Eq. (4) for asymmetric cases but  was always found to be very small. Eqs. (1), (2), and (4) refer to the transport through a single molecule of a given type (i.e., containing a given number of phenyl rings n; the label n will be suppressed in this subsection for simplicity). If all molecules (j =1, 2, . . . , N with N~100)54 in the bundle that constitutes a CP-AFM junction are characterized by the same HOMO energy offset 𝜀ℎ , Eq. (4) still holds, while Eqs. (1) and (2) should be multiplied by N (I = NI1, G = NG1, as done in Eqs. (5) and (7)). The current reads 2 𝜀ℎ,𝑗

𝐼 = 𝑉 ∑𝑁 𝑗=1 𝐺1,j 𝜀 2

(5)

2 ℎ,𝑗 −(𝑒𝑉/2)

𝜀ℎ,𝑗 =𝜀ℎ

→

𝜀2

ℎ 𝐺𝑉 𝜀2 −(𝑒𝑉/2) 2

(6)

ℎ

The zero-bias conductance G of the CP-AFM junction is given by 𝐺 = 𝐺0 ∑𝑁 𝑗=1

Γs,j Γt,j 𝜀ℎ,𝑗 =𝜀ℎ 2 𝜀ℎ,𝑗

→

𝑁𝐺0

Γ2𝑎𝑣 2 𝜀ℎ

1

2 Γ𝑎𝑣 ≡ 𝑁 ∑𝑁 𝑗=1 Γ𝑠,𝑗 Γ𝑡,𝑗

(7) (8)

Here Γ𝑎𝑣 stands for an average width level. As we will show, the model presented here combined with our experimental measurements can be employed to obtain a comprehensive set of transport parameters for OPD junctions. Table 1 presents a summary of our main results. We will refer to this table often in the following sections, which systematically address a spectrum of issues for OPD junctions including work function effects, low bias and high bias transport regimes, contact resistance, Fermi level pinning, HOMO offset, and molecule-electrode coupling. 9


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Table 1: Summary of the main results for OPD CP-AFM junctions. The resistance of the junctions [R 0 ≡ h/(2e2 ) = 12.9, k], transition voltages Vt± in V, energies (𝜀ℎ = −ε0 , ) in eV, 𝛤𝑎𝑣 (meV) obtained from Eq. (7) by assuming N=100. β-values are given per phenylene ring. Electrode

Quantity

OPD1

OPD2

OPD3

OPD4

Ag/Ag

R/R0

6.48

25.05

145.26

794.74

β=1.56

Vt+± δVt+

1.15±0.14

0.99±0.07

0.85±0.06

0.71±0.07

|Vt-±δVt-| 𝜀ℎ 𝛤𝑎𝑣 Φ±δ(ΔΦ)

1.15±0.15 1.00 39.3 -0.06±0.006

1.01±0.07 0.87 17.4 -0.12±0.010

0.83±0.08 0.73 6.1 -0.12±0.011

0.69±0.06 0.61 2.2 -0.15±0.012

Au/Au

R/R0

0.47

2.08

11.66

49.51

β=1.58

Vt+± δVt+

1.0±0.07

0.85±0.06

0.65±0.08

0.55±0.06


1.02±0.07 0.87 126.9 -0.9±0.005

0.83±0.07 0.73 50.6 -0.85±0.005

0.64±0.07 0.56 16.4 -0.9±0.007

0.54±0.06 0.47 6.7 -0.84±0.009

Pt/Pt

R/R0

0.0697

0.412

1.859

8.096

β=1.52

Vt+± δVt+

0.88±0.05

0.73±0.06

0.58±0.07

0.44±0.08


0.86± 0.06 0.75 284.1 -1.62±0.013

0.73±0.07 0.63 98.2 -1.48±0.009

0.55± 0.04 0.49 35.9 -1.41±0.007

0.42± 0.12 0.37 13.0 -1.53±0.011

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Change in Electrode Work Function ( Due to Adsorbed SAMs. Measured changes in the work function due to adsorbed OPD SAMs are collected in Table 1

A  (eV)

0.0

Ag

-0.5 Au

-1.0

-1.5

Pt 1

2

3

4

5

Number of rings (n)

SAM(eV)

B

5.0 Ag Au Pt

4.5

4.0

3.5

3.0

1

2

3

4

Number of Rings (n)

C

Ag Au Pt

0.0 -0.4

(eV)

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-0.8 -1.2 y=-0.97x+4.05 -1.6

2

R =0.95

-2.0 4.0

4.5

5.0

5.5

6.0

 (eV)

Figure 3: (A) The change in the work function ( ∆Φn = ΦSAM,n − Φ) due to OPDs (n=1, 2, 3, and 4) SAM adsorption. (B) The work function ΦSAM,n of metallic (Ag, Au, and Pt) surfaces with adsorbed OPD SAMs. (C) ∆Φn = (ΦSAM,n − Φ) versus bulk metal work function .

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and Figure 3. As visible in Figure 3A and Figure 3B, work function changes exhibit only a very weak dependence on the molecular length. On the other hand, strongly depends on the metal; the average changes (for Ag, Au, and Pt substrates are -0.11, 0.87 and -1.51 eV, respectively. These changes yield the work functions of the Φ𝑆𝐴𝑀 coated Ag, Au and Pt substrates pinned to similar values. The average Φ𝑆𝐴𝑀 values are 4.14 eV (Ag), 4.33eV (Au) and 4.14 eV (Pt), to be compared with the metal intrinsic values 4.25 eV (Ag), 5.20 eV (Au), and 5.65 eV (Pt). The strong dependence of on the type of metal is also reflected in the strong correlation between and revealed by our data, as shown in Figure 3C, which displays a linear dependence of on , with a slope of -0.97 and a correlation coefficient of 0.95. The dependence of on the type of metal is in agreement with DFT calculations,74,75 which indicate that the magnitude of the metal-thiol bond dipole strongly depends on the metal. This suggests that the change in the work function is caused by metal-S bond dipoles, and that the magnitude of the metal–S bond dipole scales almost proportionately with  a finding similar to that reported earlier for oligoacene thiols.44 The negative sign of the values measured here for OPDs is also similar to the case of oligoacenes,44 and reveals a net electron donation to the metal. This again supports the picture emerging from DFT calculations74,75 showing that the adsorption of aromatic thiolate yields a decrease in the electron density of the aromatic CS bond with a concomitant increase of the electron density of the metal-S bond. So, from this analysis, we conclude that the metal-S bond dipoles are mainly responsible for . This picture is not only consistent with previous findings on the local origin of 44 by photoelectron spectroscopy (suggesting that dipole layers at organic-metal

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interfaces could be formed within a few Å from the surface76,77), but also with a standard Helmholtz description and our quantum chemical calculations, which we present next. Within the usual picture,78 chemisorbed OPD-SAMs are modeled as two effective dipole sheets: a layer characterized by the dipole moment of the adsorbate (OPD) and another layer characterized by the dipole moment of the metal-sulfur unit (normal ⊥ ⊥ components 𝜇𝑂𝑃𝐷𝑛 and 𝜇𝑀−𝑆 ). The change in the work function obtained within this

picture based on classical electrostatics is78 N 𝑒

𝜇⊥

𝜇⊥

∆Φ = − 𝒜 𝜀 (𝜅𝑂𝑃𝐷𝑛 + 𝜅𝑀−𝑆 ) 0

𝑂𝑃𝐷𝑛

𝑀−𝑆

(9)

Here 𝜀0 is the vacuum permittivity, 𝜅𝑂𝑃𝐷𝑛 and 𝜅𝑀−𝑆 are the corresponding effective dielectric constants, and 𝑁/𝒜 denotes the number of molecules per unit area. Due to their C𝑖 -symmetry, the dipole moment of the isolated OPD1 and OPD3 molecules vanishes. The isolated OPD2 and OPD4 molecules possess non-vanishing dipole moments. Our DFT calculations yielded nearly equal values 𝜇𝑂𝑃𝐷2 =1.65 D and 𝜇𝑂𝑃𝐷4 =1.64 D. However, due to their C2-symmetry, their dipole moments are perpendicular to the molecular axis. Because the molecular axis is almost normal to ⊥ electrodes’ surface (𝜇𝑂𝑃𝐷𝑛 = 𝜇𝑂𝑃𝐷𝑛 sin 𝜑 ≃ 0, cf. Figure S2B and the small -values

given in SI), the first term in the parenthesis entering Eq. (9) (practically) vanishes. The fact that this term is negligible explains why the experimental  values do not notably depend on the molecular size n (cf. Table 1 and Figure 3A) and supports the idea that primarily originates from dipoles localized at the metal-S contacts rather than from the intrinsic molecular dipoles. The fact that the magnitude and even the sign of substantially depend on the type of metal traces back to specific character of the charge transfer between the sulfur atom and the contacting metal. 13


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Charge Transport: Low Bias Range (V up to ±0.1 V). We switch now to the transport results. Detailed separate analysis and discussion of the low and high voltage ranges follow below. Our results for the low-bias resistance are presented in Figure 4. In discussing these results, we will separately consider the impact of the backbone (the molecular size n), and the contacts. The low-bias resistance 𝑅𝑛 ≡ 𝑅𝑂𝑃𝐷𝑛 = 𝑅 will be analyzed by resorting to the factorization scheme35,44,53,54 𝑅𝑛 = 𝑅𝑐 exp(𝛽𝑛)

(10)

which is convenient because it disentangles the length (exponential) dependence from the effective contact contribution 𝑅𝑐 . It is a general feature of non-resonant tunneling, which characterizes all our junctions. It is worth noting that our transport data exhibit neither (Arrhenius) temperature dependence nor crossover to an Rn linearly dependent on n; a crossover from (non-resonant) tunneling to conduction via hopping can only be expected at larger sizes.5,15,79–81 From the slope of the semilogarithmic plot of 𝑅 = 𝑅𝑛 versus molecular size n one can determine the tunneling attenuation factor β, and its intercept at n = 0 gives the effective contact resistance 𝑅𝑐 . Tunneling Attenuation Factor,  . Figure 4A displays a semilog plot of resistance versus number of phenyl rings for OPD junctions. Resistances were calculated from the average of about 150-250 I-V traces within ±0.1 V. The linear relationships in this figure indicate that the data are well explained within the non-resonant tunneling picture underlying Eq. (10). Within experimental uncertainties, the  values found here are independent of metal work functions, as reported previously.35,44,82,83 This implies that the difference of the HOMO energy offsets (“barriers” for charge transport) caused by the different contact

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A Resistance ()

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107 106

RC

105 10

4

10

3

102

Ag/Ag1.56 Au/Ag1.65 Ag/Pt 1.58 Au/Au1.58 Au/Pt 1.63 Pt/Pt 1.52

=1.58/ring 0.37/Å

B Resistance ()

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107 106 10

5

104

1

2

3

4

ROPD2 ROPD1 RC

103 102

0

ROPD4 ROPD3

5

Tip Sub

8

Ag Ag

Au Ag

9

Ag Pt

Au Au

10

Au Pt

Pt Pt

11

Sum of electrode work function (eV)

Number of Rings (n)

Figure 4: (A) Semilog plot of low bias resistance versus number of phenyl rings (n). The insert shows the coated tip/substrate metals and the respective -values of each junction. (B) Semilog plot of molecular resistance (R OPDn , n=1, 2, 3 and 4) and contact resistance (RC) vs. the sum of the work functions of the two electrodes.

metals is not significant enough to vary the 𝛽 values. Indeed, the pinning effect that appears in other conjugated oligoacenes44 is also found in this case, as will be clarified below. The average value determined from the slopes of the semilog plots of Figure 4A is 𝛽 = 1.58/ring = 0.37 Å−1. Previous studies of CP-AFM junctions based on oligophenylene monothiols and metallic electrodes found values 𝛽 = 0.41−0.61 Å−1.36,84 The present result for 𝛽 is in line with the fact that, unlike in the case of saturated (e.g., alkane) backbones (𝛽 values for alkane mono- and dithiols do not differ35), 𝛽 values for CP-AFM junctions based on conjugated backbones with two thiol anchoring groups are smaller than those of monothiols. For the higher conjugated oligoacenes, the 𝛽 values are 0.2 Å−1 and 0.5 Å−1 for dithiols and monothiols, respectively.44 So, the present finding indicates that, for molecules with delocalized electrons, is not only a backbone property, as it also depends on the number of thiol contacting groups.44 Contact Resistance vs. Metal Work Function. The contact resistance 𝑅𝑐 determined from the zero length intercept clearly indicates the important role of the type of 15


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electrodes. As visible in Table S2 and Figure 4B, the bare electrode work function has a dramatic effect on the contact resistance 𝑅𝑐 (and implicitly on 𝑅𝑂𝑃𝐷𝑛 ). For the electrodes studied (Ag, Au, and Pt) increases by 1.4 eV, and this manifests itself in (contact) resistance decreasing by a factor of ~70. As noted earlier, the opposite variations in and R reveal a hole (p-type, HOMO-mediated) conduction. This dramatic decrease in 𝑅𝑐 with for oligophenylene dithiol junctions is comparable to that of our previous studies on alkane dithiol- and oligoacene dithiol-based CP-AFM junctions.35,44 For monothiol-based junctions of alkanes or oligoacenes and the same electrodes as those used here, the decrease in 𝑅𝑐 is even larger (by about 3 orders of magnitude).35,44,55 However, no significant 𝛽 value changes were found in those previous results. This indicates that the 𝛽 values are much less sensitive to the level alignment than the effective contact resistance in those junctions. General I-V behavior. Figure 5 and Figure S8 display representative I-V characteristics of our CP-AFM junctions based on OPDs and various metallic electrodes (s, t = Ag, Au or Pt). I-V traces are nearly symmetric with respect to the origin and exhibit a nonlinearity that becomes more pronounced at higher biases. For a given bias, the current decreases exponentially with the length. The currents for junctions based on a given molecular species (OPD) increase as the electrodes’ work function increases. These attributes indicate hole (HOMO-mediated) conduction and a non-resonant tunneling mechanism. As evidence of the unipolar conduction (mediated by HOMO and negligible LUMO contribution, Figure 2), we refer to the UV/visible absorption measurements (Figure S5). Indeed, the values found for the optical gap (3.5-3.9 eV) and the HOMO

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10

A

B

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ln(I/V2)

Current (A)

Ag/Ag

0

-0.8

-0.4

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OPD4

-6 -5 -4 -3 -2 -1 0

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1/V (V-1)

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Au/Au

OPD1

50

0

OPD1 OPD2 OPD3 OPD4

-50

-100

-0.8

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ln(I/V2)

Current (A)

OPD3

-15

Au/Au

OPD2

-9 -10

OPD3

-11

OPD4

-12

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-6 -5 -4 -3 -2 -1 0

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400

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F -7

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E

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-14

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100

OPD1

-11

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C

Ag/Ag

-13

OPD1 OPD2 OPD3 OPD4

-5

-10

Current (A)

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-8

OPD2 -9

OPD3 -10

OPD4 -11 -6 -5 -4 -3 -2 -1 0

0.8

1

1/V (V-1)

Tip bias (V)

2

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6

Figure 5: Representative 𝐼 − 𝑉 and transition voltage (ln(𝐼/𝑉 2 ) vs. 1/V) spectra obtained by averaging 25 I − V traces for (A) and (B) Ag-OPDn-Ag, (C) and (D ) Au-OPDn-Au, (E) and (F) Pt-OPDn-Pt CP-AFM junctions. Transition voltages (𝑉𝑡 ) are indicated by lines joining the minima.

energy offsets 𝜀ℎ (at most 1 eV below the Fermi level, cf. Table 1) yield a LUMO located substantially higher above the Fermi level. It is worth emphasizing here that the LUMO positions depicted in Figure 2 are rather crude estimations; nevertheless, they illustrate the fact that the LUMOs are significantly more distant from the Fermi level than the

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HOMOs, in agreement with the various consistency tests done across the paper, which support the p-type conduction in our OPD-junctions. One should still note that, as shown recently, because the exciton binding energy is substantial at the molecular sizes considered,85 the transport HOMO-LUMO gap is larger than the optical HOMO-LUMO gap; that is, the relevant LUMO energies are even higher than that shown in Figures 2 and S7. Non-Linear Bias Range (|V|>0.1 V); TVS and Analysis of the HOMO Energy Offset. In the analysis of the nonlinear transport, we pay special attention to the transition voltage 𝑉𝑡 that our group proposed a few years ago.49 𝑉𝑡 is the key quantity of so-called transition voltage spectroscopy (TVS). Due to its simplicity and reproducibility, a series of groups have utilized TVS as a tool for quantifying the molecular orbital energy offset relative to the electrodes’ Fermi energy.5,32,47,48,50,56–58,69,86–92 The transition voltage, defined as the bias at the minimum of the Fowler-Nordheim quantity ln(𝐼/𝑉 2 ) ,49 quantifies the I –V nonlinearity: it corresponds to the point where the differential conductance is two times larger than the pseudo-ohmic conductance.93

I V

2 V Vt

I V

(11) V Vt

Typical TVS spectra of the oligophenylene dithiol junctions are obtained by recasting the measured I-V curves of Figure 5A, C, E in Fowler-Nordheim (FN) coordinates ln(𝐼/𝑉 2 ) vs. 1/V, as depicted in Figure 5B, D, F. These FN plots exhibit well-defined minima, which are (practically) symmetric with respect to the bias polarity (𝑉𝑡 = 𝑉𝑡+ ≃ −𝑉𝑡− ). Based on Eq. (S1), the Vt symmetry with respect to bias polarity reversal indicates that γ≈0, and via Eq. (3) that the applied voltage does not notably shift the HOMO energy.

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The experimental results for 𝑉𝑡 are collected in Table 1 and visualized in Figure 6. The values of the HOMO energy offset 𝜀ℎ deduced from the experimental 𝑉𝑡 data via TVS, Eq. (4), are also included in Table 1 and Figure 7. The fact that the theoretical model employed, which underlines Eq. (4), is able to reproduce the measured I-V curves (see below) makes us confident of the TVS-based estimates for 𝜀ℎ (see also the discussion of Section Remarks on the Theoretical Modeling of Transport in the SI). As further support, it is worth noting that, for all M-OPD1-M junctions investigated here

A

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4.2

4.5

4.8

5.1

5.4

5.7

 (eV)

Number of rings (n)

Figure 6: Transition voltages Vt± of HOMO-metal M-OPDn-M junctions (M=Ag, Au, Pt) as a function of (A) molecular length, (B) bare electrode work function.

(M=Ag, Au, Pt), the present TVS-based estimates agree very well with the values directly measured by UPS

44

(see Table 2). Because the UPS and CP-AFM setups are not

equivalent (one metallic contact vs. two metallic contacts, respectively), a difference between the corresponding h-values may exist. To check whether this difference is significant, we have performed EOM-IP-CCSD calculations for an OPD1 molecule having gold atoms covalently bonded to one (Au-OPD1) or two (Au-OPD1-Au) thiol groups; the lowest ionization energies were found to differ only by 80 meV.

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Table 2: Values (in eV) of HOMO energy offsets h=EF-EHOMO of OPD1 and different metals deduced in the present work via TVS and direct UPS data (cf. Table 1 of ref. 44 noting that OPD1 is denoted Ph(SH)2 there). Method

Ag

Au

Pt

TVS

1.0±0.13

0.88±0.05

0.75±0.04

UPS

1.1

0.9

0.8

Based on Φ𝑆𝐴𝑀 (SKPM), the optical band gap (UV-visible), and 𝜀ℎ obtained from Eq. (4), the energy level alignments for OPD SAMs on Ag, Au, and Pt are well-defined (see Figure S7), which is essential for understanding the charge transport properties in molecular junctions. As already encountered for other aromatic molecules,5,44,50,86,87 we found that 𝑉𝑡 decreases with increasing number of phenyl rings n, see Figure 6A. This implies via Eq. (4) a HOMO closer to the Fermi level with increasing n, as depicted in Figure 7A. This is related to the decrease in the optical gap observed in UV-visible absorption and is also typical of other aromatic systems.5,44,79 As shown in Figure S5, UV-visible absorption measurements for OPDn confirm the decrease of the optical gap with increasing size n. The fact that absolute values of 𝑉𝑡 and 𝜀ℎ decrease as the electrode work function Φ increases (cf. Figure 6B and Figure 7B) is of course another indication that the charge transport through OPDn is mediated by the HOMO. For electromigrated benzene dithiol (OPD1) junctions, the p-type HOMO-mediated conduction has been demonstrated by electrostatic gating.56 Because of the linear correlation between  and we are able to plot the linear correlations of ln R, 𝑉𝑡 and 𝜀ℎ versus (Figure S9). 20


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To end this section, we briefly compare our present results for Au-OPD-Au junctions with existing reports in the literature.56–60 Here, it is important to distinguish between the magnitude of the currents (conductances) and the transition voltages. The

1.2 Average slope= -0.13 0.01

Ag/Ag Au/Au Pt/Pt

1.0 0.8 0.6

B

h= -0 (eV)

A

h= -0 (eV)

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1.2 1.0 0.8 0.6

0.4

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Au/Au

Ag/Ag

1

OPD1 OPD2 OPD3 OPD4

Average slope= -0.18 0.02

4.8

5.1

5.4

5.7

(eV)

Number of rings (n)

Figure 7: The HOMO energy offset ε0 = EHOMO − EF deduced via TVS for OPD molecules embedded in homo-metal CP-AFM junctions as a function of (A) the molecular length, (B) the electrode work function .

currents measured by us are up to two order of magnitudes larger than those found for electromigrated junctions56 and STM junctions.57–60 Basically, this difference reflects the larger number of molecules (~100 in our CP-AFM junctions. By contrast, the present values of Vt are consistent with those deduced for electromigrated BDT≡OPD1 (𝑉𝑡 =1.14±0.04 V)56 and STM biphenyl≡OPD2 (𝑉𝑡 =0.91±0.031V).58 These values agree well with the corresponding values 𝑉𝑡 =1.02±0.07V and 𝑉𝑡 =0.84±0.07V of Table 1. On this basis, we can reiterate a statement made earlier:44,48 much more than the (low-bias) conductance, the transition voltage does represent a molecular signature. Let us further elaborate on this point. We have just mentioned that, in contrast to the similar values of the transition voltage Vt (which are indistinguishable within experimental errors), the low-bias conductance exhibits a significant dependence on the 21


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experimental platform (CP-AFM, STM, electromigration). The interpretation of this behavior, which fits the present theoretical framework, is the following. The (HOMO) widths Γ are setup dependent (they are determined to the molecule-electrode couplings, cf. Eq. (13) below), and this makes the low-bias conductance G platform dependent (cf. Eqs. (2) and (7)). However, as long as Г remains smaller than the HOMO offset ε h (i.e., nonresonant tunneling limit), Г does not affect Vt, which is only determined by εh, as expressed by Eq. (4). (Remember that Eqs. (4), (S1), and (S2) are deduced just by assuming Γ

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